Semi-symmetric isotopic closure of some group varieties and the corresponding identities

Krainichuk Halyna; Tarkovska Olena

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Articolul precedent

Articolul urmator

892

Ultima descărcare din IBN:
2023-06-30 14:04

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similare conform CZU

512.54+512.548 (3)

Algebră (410)

SM ISO690:2012

KRAINICHUK, Halyna, TARKOVSKA, Olena. Semi-symmetric isotopic closure of some group varieties and the corresponding identities. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2017, nr. 3(85), pp. 3-22. ISSN 1024-7696.

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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica

Numărul 3(85) / 2017 / ISSN 1024-7696 /ISSNe 2587-4322

Semi-symmetric isotopic closure of some group varieties and the corresponding identities

CZU: 512.54+512.548

MSC 2010: 34C05, 58F14.

Pag. 3-22

Krainichuk Halyna, Tarkovska Olena

Vasyl Stus Donetsk National University

Disponibil în IBN: 10 februarie 2018

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Rezumat

Four families of pairwise equivalent identities are given and analyzed. Every identity from each of these families defines one of the following varieties: 1) the semi-symmetric isotopic closure of the variety of all Boolean groups; 2) the semisymmetric isotopic closure of the variety of all Abelian groups; 3) the semi-symmetric isotopic closure of the variety of all groups; 4) the variety of all semi-symmetric quasigroups. It is proved that these varieties are different and form a chain. Quasigroups belonging to these varieties are described. In particular, quasigroups from 1) and 2) varieties are medial and in addition, they are either groups or non-commutative semi-symmetric quasigroups.

Cuvinte-cheie
Group, quasigroup, identity, variety,

isotopic closure, totally symmetric, semi-symmetric, commutative.

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